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3 years ago

Simplify assuming x is a positive number √x^16+16x^8

Mathematics

1 answer:

bogdanovich [222]3 years ago

4 0

$\sqrt{x^{16} + 16x^8}$

$\sqrt{x^8(x^{8} + 16)}$

$x^4\sqrt{(x^{8} + 16)}$

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Can i get help on 18 & 22 please

Pavlova-9 [17]

18) 36.36 rounded it is 36.4

22)53.71 rounded it it’s just 53.7

5 0

3 years ago

When building a house, the number of days required to build varies inversely with with the number of workers. One house was buil

Helga [31]

Let d represent number of days and n represent number of workers.

We have been given that when building a house, the number of days required to build varies inversely with with the number of workers.

We know that the equation $y=\frac{k}{x}$ represents the relation where y is inversely proportional to x and k is the constant of proportionality.

So our required equation would be $d=\frac{k}{n}$

Upon substituting our given values, we will get:

$19=\frac{k}{35}$

$k=19\cdot 35$

$k=665$

Since constant of proportionality is 665, so our equation would be $d=\frac{665}{n}$ .

To find the number of days it will take to build a similar house with 5 workers, we will substitute $n=5$ in our equation as:

$d=\frac{665}{5}$

$d=133$

Therefore, it will take 133 days for 5 workers to build a similar house.

5 0

3 years ago

Apply Crammer's Rule to find the solution to the following quations .2x + 3y = 1, 3x + y = 5

Bond [772]

Answer:

The solution to the equation system given is:

<u>x = 2</u>
<u>y = -1</u>

Step-by-step explanation:

First, we must know the equations given:

2x + 3y = 1
3x + y = 5

Following Crammer's Rule, we have the matrix form:

$\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] =\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}1\\5\end{array}\right]$

Now we solve using the determinants:

$x=\frac{\left[\begin{array}{ccc}1&3\\5&1\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(1*1)-(5*3)}{(2*1)-(3*3)} = \frac{1-15}{2-9} =\frac{-14}{-7} = 2$

$y=\frac{\left[\begin{array}{ccc}2&1\\3&5\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(2*5)-(3*1)}{(2*1)-(3*3)}=\frac{10-3}{2-9} =\frac{7}{-7}=-1$

Now, we can find the answer which is x= 2 and y= -1, we can replace these values in the equation to confirm the results are right, with the first equation:

2x + 3y = 1
2(2) + 3(-1)= 1
4 - 3 = 1
1 = 1

And, with the second equation:

3x + y = 5
3(2) + (-1) = 5
6 - 1 = 5
5 = 5

4 0

3 years ago

max bought 2 3/4 punds of green apples, 1 5/8 pounds of yellow apples, and 1 5/8 pounds red apples. the total cost was $5.40. wh

dangina [55]

2 3/4 + 1 5/8 + 1 5/8 =
2 + 1 + 1 = 4 (add the whole numbers)
3/4 + 5/8 + 5/8 = 6/8 + 5/8 + 5/8 = 16/8 = 2 (add the fractions)
4 + 2 = 6 total lbs

5.40 for 6 lbs = 5.40/6 = 0.90 (so the apples cost 90 cents per lb)

7 0

3 years ago

Please please help!!!

Rashid [163]

Answer:

1/2

Step-by-step explanation:

cos(θ) = √(1 -sin(θ)²) = √(1 -3/4) = √(1/4)

cos(θ) = 1/2

3 0

3 years ago